Simplify the following expression: $ q = \dfrac{k + 1}{-9k + 3} - 9 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{-9k + 3}{-9k + 3}$ $ \dfrac{9}{1} \times \dfrac{-9k + 3}{-9k + 3} = \dfrac{-81k + 27}{-9k + 3} $ Therefore $ q = \dfrac{k + 1}{-9k + 3} - \dfrac{-81k + 27}{-9k + 3} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{k + 1 - (-81k + 27) }{-9k + 3} $ Distribute the negative sign: $q = \dfrac{k + 1 + 81k - 27}{-9k + 3}$ $q = \dfrac{82k - 26}{-9k + 3}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-82k + 26}{9k - 3}$